Combine dry ingredients in a large mixing bowl.,Add applesauce and margarine.,Using an electric mixer, beat 2 minutes, scraping bowl and beaters occasionally.,Add eggs and beat 2 minutes.,Stir in carrots and nuts, blending well.,Pour into a 9-inch square baking pan that has been sprayed with nonstick spray.,Bake at 350° for 50-55 minutes, or until a toothpick inserted near the center comes out clean.,Let cake cool.,______,Add applesauce and beat until smooth.,Frost cooled cake.